Abelian representation for nonabelian Wilson loops and the Non - Abelian Stokes theorem on the lattice

摘要

We derive the Abelian - like expression for the lattice SU(N) Wilson loop inarbitrary irreducible representation. The continuum Abelian representation ofthe SU(N) Wilson loop (for the loop without selfintersections) that has beenobtained by Diakonov and Petrov appears to be a continuum limit of thisexpression. We also obtain the lattice variant of a non - Abelian Stokestheorem and present the explicit expression for the matrix $\cal H$ used in theDiakonov - Petrov approach.